College administrations are continually perplexed about how to deal with hazing issues on their campuses. But howwidespread is hazing, and, in fact, what constitutes hazing anyway? One study tried to get an objective handle onthis persistent college phenomenon by carrying out a large survey of college and university students on 53campuses. The study leaders defined hazing as "any activity expected of someone joining or participating in a groupthat humiliates, degrades, abuses, or endangers them regardless of a person's willingness to participate."The two types of activities receiving the highest rate of participation overall were "participate in a drinking game" and"sing or chant by yourself or with a few selected team members in a public situation that is not related to the event,game, or practice." The table below shows the sample sizes for those responding and the proportions for eachactivity across a variety of typical campus groups. In comparing these groups, regard the samples as beingindependent even though some of the same students may be in more than one group.Campus GroupDrinking Game Sing or ChantVarsity athletics0.276400.45Social fraternity or sorority12980.550.32Service fraternity or sorority 5440.260.18Intramural sports10600.280.13Performing arts8210.230.26Academic clubs10610.100.06a. Estimate the difference, with 95% confidence, between the proportions engaged in drinking games among thosein varsity athletics as compared to those in social fraternities or sororities.Round the answers to three decimal places.< Pfraterninies - PvarsitiesDo the same for those who have been involved in singing or chanting.Round the answers to three decimal places.< Pfraterninies Pvarsities «b. Estimate the difference, with 90% confidence, between the proportions engaged in drinking games among thosein service fraternities or sororities as compared to those in performing arts.< Pfraterninies - Parts «Do the same for those who have been involved in singing or chanting.< Parts - Pfraterninies

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 13PT

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College administrations are continually perplexed about how to deal with hazing issues on their campuses. But how
widespread is hazing, and, in fact, what constitutes hazing anyway? One study tried to get an objective handle on
this persistent college phenomenon by carrying out a large survey of college and university students on 53
campuses. The study leaders defined hazing as "any activity expected of someone joining or participating in a group
that humiliates, degrades, abuses, or endangers them regardless of a person's willingness to participate."
The two types of activities receiving the highest rate of participation overall were "participate in a drinking game" and
"sing or chant by yourself or with a few selected team members in a public situation that is not related to the event,
game, or practice." The table below shows the sample sizes for those responding and the proportions for each
activity across a variety of typical campus groups. In comparing these groups, regard the samples as being
independent even though some of the same students may be in more than one group.
Campus Group
Drinking Game Sing or Chant
Varsity athletics
0.27
640
0.45
Social fraternity or sorority
1298
0.55
0.32
Service fraternity or sorority 544
0.26
0.18
Intramural sports
1060
0.28
0.13
Performing arts
821
0.23
0.26
Academic clubs
1061
0.10
0.06
a. Estimate the difference, with 95% confidence, between the proportions engaged in drinking games among those
in varsity athletics as compared to those in social fraternities or sororities.
Round the answers to three decimal places.
< Pfraterninies - Pvarsities
Do the same for those who have been involved in singing or chanting.
Round the answers to three decimal places.
< Pfraterninies Pvarsities «
b. Estimate the difference, with 90% confidence, between the proportions engaged in drinking games among those
in service fraternities or sororities as compared to those in performing arts.
< Pfraterninies - Parts «
Do the same for those who have been involved in singing or chanting.
< Parts - Pfraterninies

Expert Solution

Step 1

Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case you require the unanswered parts also, kindly re-post that parts separately.

95% confidence interval for the difference between the proportions engaged in drinking games among those in varsity athletics as compared to those in social fraternities or sororities is,

From the given information,

${\hat{p}}_{1} = 0.55 {\hat{p}}_{2} = 0.45 n 1 = 1298 n 2 = 640$

Consider,

$p = \frac{n 1 {\hat{p}}_{1} + n 2 {\hat{p}}_{2}}{n 1 + n 2} = \frac{(640 * 0.45) + (1298 * 0.55)}{1298 + 640} = 0.517$

Critical value=1.96

$95 % C I = {\hat{p}}_{1} - {\hat{p}}_{2} \pm z_{c r i t i c a l} \sqrt{p (1 - p) (\frac{1}{n 1} + \frac{1}{n 2})} = 0.55 - 0.45 \pm 1.96 \sqrt{0.517 (1 - 0.517) (\frac{1}{1298} + \frac{1}{640})} = 0.1 \pm 0.0473 = (0.053, 0.147)$

Step 2

95% confidence interval for the difference between the proportions involved in singing or chanting among those in varsity athletics as compared to those in social fraternities or sororities is,

From the given information,

${\hat{p}}_{1} = 0.32 {\hat{p}}_{2} = 0.27 n 1 = 1298 n 2 = 640$

Consider,

$p = \frac{n 1 {\hat{p}}_{1} + n 2 {\hat{p}}_{2}}{n 1 + n 2} = \frac{(640 * 0.27) + (1298 * 0.32)}{1298 + 640} = 0.303$

Critical value=1.96

$95 % C I = {\hat{p}}_{1} - {\hat{p}}_{2} \pm z_{c r i t i c a l} \sqrt{p (1 - p) (\frac{1}{n 1} + \frac{1}{n 2})} = 0.32 - 0.27 \pm 1.96 \sqrt{0.303 (1 - 0.303) (\frac{1}{1298} + \frac{1}{640})} = 0.1 \pm 0.0439 = (0.006, 0.094)$

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